Find the general solution to the differential equation

Find the general solution to the differential equation

y'+10x^9y=x^10

Use the variable I=∫e^x^10 dx where it occurs in your answer.

y' + 10x⁹ y= x¹⁰
I = e^(∫10x⁹ dx) = e^(x¹⁰)

y' + 10x⁹ y= x¹⁰
y'e^(x¹⁰) + 10x⁹e^(x¹⁰) y= x¹⁰ e^(x¹⁰)

[ ye^(x¹⁰) ] ' = x¹⁰ e^(x¹⁰)

∫ [ ye^(x¹⁰) ] ' = ∫ x¹⁰ e^(x¹⁰) dx

to integrate the right-hand side use ∫vdu = uv - ∫udv
∫ [ ye^(x¹⁰) ] ' = ∫ x¹⁰ e^(x¹⁰) dx

ye^(x¹⁰) = xe^x - e^x + constant
y = Ce^(-x¹⁰) + [ (x - 1)e^x - e^x ] / e^(x¹⁰)

y = e^(- x^10 )[ int { x^10 e^(x^10 )+ C ]....IF = e^ ( x^10 )